Search any question & find its solution
Question:
Answered & Verified by Expert
25 capacitors each of capacitance $1 \mu \mathrm{F}$ are connected in series to a battery of $100 \mathrm{~V}$. The total charge stored on capacitors is
Options:
Solution:
1533 Upvotes
Verified Answer
The correct answer is:
$4.0 \times 10^{-6} \mathrm{C}$
The given situation is shown below.
In series combination, equivalent capacity is given by
$$
\begin{aligned}
\frac{1}{C_{\mathrm{eq}}} & =\frac{1}{C_1}+\frac{1}{C_2}+\ldots .+\frac{1}{C_{25}} \\
& =\frac{1}{1 \times 10^{-6}}+\frac{1}{1 \times 10^{-6}}+\ldots .+25 \text { terms } \\
& =\frac{25}{1 \times 10^{-6}} \quad\left(\therefore C=1 \times 10^{-6} \mathrm{~F}\right)
\end{aligned}
$$
or $C_{\mathrm{eq}}=\frac{1}{25} \times 10^{-6}=4 \times 10^{-8} \mathrm{~F}$
Now, given potential difference across this combination, $V=100 \mathrm{~V}$
So, charge on combination
$$
\begin{aligned}
Q & =C_{\mathrm{eq}} V=4 \times 10^{-8} \times 100 \\
& =4 \times 10^{-6} \mathrm{C}
\end{aligned}
$$
In series combination, equivalent capacity is given by
$$
\begin{aligned}
\frac{1}{C_{\mathrm{eq}}} & =\frac{1}{C_1}+\frac{1}{C_2}+\ldots .+\frac{1}{C_{25}} \\
& =\frac{1}{1 \times 10^{-6}}+\frac{1}{1 \times 10^{-6}}+\ldots .+25 \text { terms } \\
& =\frac{25}{1 \times 10^{-6}} \quad\left(\therefore C=1 \times 10^{-6} \mathrm{~F}\right)
\end{aligned}
$$
or $C_{\mathrm{eq}}=\frac{1}{25} \times 10^{-6}=4 \times 10^{-8} \mathrm{~F}$
Now, given potential difference across this combination, $V=100 \mathrm{~V}$
So, charge on combination
$$
\begin{aligned}
Q & =C_{\mathrm{eq}} V=4 \times 10^{-8} \times 100 \\
& =4 \times 10^{-6} \mathrm{C}
\end{aligned}
$$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.